Synthesis of new binary trimethoxyphenylfuran pyrimidinones as proficient and sustainable corrosion inhibitors for carbon steel in acidic medium: experimental, surface morphology analysis, and theoretical studies

In this study, synthesis and assessment of the corrosion inhibition of four new binary heterocyclic pyrimidinones on CS in 1.0 M hydrochloric acid solutions at various temperatures (30–50 °C) were investigated. The synthesized molecules were designed and synthesized through Suzuki coupling reaction, the products were identified as 5-((5-(3,4,5-trimethoxyphenyl)furan-2-yl)methylene)pyrimidine-2,4,6(1H,3H,5H)-trione (HM-1221), 2-thioxo-5-((5-(3,4,5-trimethoxyphenyl)furan-2-yl)methylene)dihydropyrimidine-4,6(1H,5H)-dione (HM-1222), 1,3-diethyl-2-thioxo-5-((5-(3,4,5-trimethoxyphenyl)furan-2-yl)methylene)dihydropyrimidine-4,6(1H,5H)-dione (HM-1223) and 1,3-dimethyl-5-((5-(3,4,5-trimethoxyphenyl)furan-2-yl)methylene)pyrimidine-2,4,6(1H,3H,5H)-trione (HM-1224). The experiments include weight loss measurements (WL), electrochemical impedance spectroscopy (EIS) and potentiodynamic polarization (PDP). From the measurements, it can be shown that the inhibition efficiency (η) of these organic derivatives increases with increasing the doses of inhibitors. The highest η recorded from EIS technique were 89.3%, 90.0%, 92.9% and 89.7% at a concentration of 11 × 10−6 M and 298 K for HM-1221, HM-1222, HM-1223, and HM-1224, respectively. The adsorption of the considered derivatives fit to the Langmuir adsorption isotherm. Since the ΔGoads values were found to be between − 20.1 and − 26.1 kJ mol−1, the analyzed isotherm plots demonstrated that the adsorption process for these derivatives on CS surface is a mixed-type inhibitors. Scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDX), atomic force microscope (AFM) and Fourier- transform infrared spectroscopy (FTIR) were utilized to study the surface morphology, whereby, quantum chemical analysis can support the mechanism of inhibition. DFT data and experimental findings were found in consistent agreement. Graphical Abstract Supplementary Information The online version contains supplementary material available at 10.1186/s13065-024-01280-6.


Introduction
Corrosion is a natural phenomenon [1][2][3] in which metals and alloys transform into more stable forms such as oxides and sulfides by reacting directly with the surrounding environment [4,5].However, some metallic components exposed to corrosive aqueous media, especially in acidic conditions, may suffer severe degradation of their properties and durability, leading to the disintegration of CS and failures [6].Corrosion has significant implications for human safety [7] and various industries due to its negative impact, notably the gas and oil sector, making it a critical area of research [8].Carbon steel (CS) is a vital component in construction and industrial field [9][10][11][12] due to its high mechanical properties, low temperature toughness, hydrogen-induced crack and fracture resistances, weldability [13] and remarkable economy, besides the possibilities for its environmental, technical and economic recycling in the concrete production industry [14][15][16].However, one of the major drawbacks of using CS is its high susceptibility to corrosion in corrosive conditions, such as during the pickling process using HCl [17][18][19], which is widely employed in industries such as chemical cleaning [20], pickling iron, boiler descaling, scrubbing, [21,22] and oil well acidification [23,24].Nevertheless, carbon steel corrosion is an inevitable but controllable phenomenon [22].Among the available methods for corrosion control in acidic solutions, the use of inhibitors is considered an effective approach for protecting metals from corrosion [25].Organic inhibitors containing π conjugated electrons, aromatic rings and heteroatoms are commonly used to prevent metal corrosion [26][27][28][29].Organic scaffolds containing active sites such as oxygen, nitrogen and sulfur in their structures show higher inhibitory efficiency than other molecules having only a single heteroatom [30] through either chemical, physical or both adsorption mechanisms on the metal surface [31][32][33].The aforementioned inhibitors block the active sites on the CS surface by forming protective coating layers [34] and reducing the corrosive effects [35].The adsorption process can be influenced by the inhibitor structure [36], the nature of the metal surface, and the type of corrosive conditions [37].Motivated by the above-mentioned aspects, the synthesis and investigation of new eco-friendly corrosion inhibitors is highly desirable, as the application of green chemistry is essential to the field of corrosion research.The percentages of inhibition efficiency (η) of some reported analogues of pyrimidine derivatives are shown in Table 1.
The aim of the present work was to design and investigate new synthesized trimethoxyphenylfuran pyrimidinone derivatives as potential CS corrosion inhibitors at low concentrations in an acidic medium.This study involved electrochemical measurements, weight loss analysis, and surface examination of CS using AFM, SEM, FTIR and EDX methods.Moreover, the thermodynamic and kinetic parameters were calculated and discussed.The adsorption of four furan pyrimidinone scaffolds on the CS was also investigated at different soaking times to understand the interactions between the furylidene-pyrimidinone scaffolds and the CS surface.Furthermore, the proposed mechanism for corrosion inhibition was elucidated by quantum chemistry calculations for the four furylidene-pyrimidinone derivatives.Ultimately, we aimed to use these inhibitors to prevent pipeline corrosion and rusting in various industrial processes.

Materials
Table 2 illustrates the molecular structures, formulas, molecular weights, yield, shape and melting point (m.p.) of four novel furylidene-pyrimidinone derivatives, HM-1221, HM-1222, HM-1223, and HM-1224.The synthesis and characterization in details are shown in the experimental section.(For IR, NMR, and Mass Table 1 Literature reviews on the corrosion inhibition behavior of similar pyrimidine derivatives studied before spectra of the investigated inhibitors see the supplementary material).

Materials
Corrosion inhibition experiments have been carried out on CS with the following chemical composition (wt.%): (C: 0.07, Si: 0.05, Ti: 0.001, Mn: 0.3, Al: 0.03, S: 0.01, P: 0.022, and Fe balance).The materials were cut into coupons of size 2 cm × 2 cm × 0.2 cm for the WL tests.The working electrode used in surface morphology and electrochemical studies has an exposed area of 1 cm 2 .All the chemicals and reagents were purchased from Sigma-Aldrich Chemicals, all were of analytical grade, and solutions were prepared using double distilled water.

Solutions
One molar HCl (37%) stock solution was made by dilution with double-distilled water.The synthesized compounds were dispersed in a combination of 5 mL DMSO and 25 mL EtOH to generate a stock solution of dosage inhibitors with a concentration of 1 × 10 −3 M. Furthermore, the concentration varieties of the studied compounds were (1 × 10 -6 -11 × 10 -6 M) and were prepared by dilution.

Weight loss (WL) method
We measured WL using CS specimens at (30-50 °C) temperatures.Prior to being submerged in the test solution, the CS surface was polished using sandpaper grades (320-2000), cleaned with distilled water, allowed to dry at ambient temperature, and weighed.CS specimens were weighed before and after immersion in 100 mL of 1.0 M HCl without and with varied inhibitor dosages every 30 min for 3 h.The following equations were used to determine CR, θ, and η [43][44][45][46]: whereas, W and A represent specimen WL (mg) and area (cm 2 ), CR and CR (i) represent CS corrosion rate (mg cm −2 h −1 ) without and with inhibitors, and t represents exposure duration (h), θ degree of surface coverage.

Electrochemical measurements
In order to record and retain data, electrochemical procedures were done utilizing Potentiostat/Galvanostat (Gamry PCI300 ̸ 4) that include DC 105 software for PDP and EIS 300 programs for EIS measurements, is linked to a computer for data recording and storage.Electrochemical methods using EIS and PDP in 1.0 M HCl without and with varying inhibitor dosages at ambient temperature were used to study CS corrosion.The standard electrochemical cell has three glass vessels with a platinum wire (auxiliary electrode), a saturated calomel electrode, SCE, (reference electrode), and CS (working electrode).The exposed surface area of the working electrode was 1cm 2 .It was weld from one side to Cu-wire which used for (1) (3) η WL = θ × 100 electric connection.The samples were embedded in glass tube of just larger diameter than the samples then epoxy resin was used to stick the sample to glass tube.While, the chemical composition of the working electrode utilized in electrochemical methods was the same for the CS in weight loss.For 30 min, the CS electrode was submerged in the test solution to achieve a constant open circuit potential (OCP).Polarization studies were conducted in the potential range from − 250 mV to 250 mV vs. OCP above OCP at a scan rate of 0.5 mV s −1 scan rate.Corrosion current density (i corr ) and corrosion potential (E corr ) were assessed from the interplay of the correlation anodic and cathodic sections of Tafel plots in the presence and absence of altered inhibitor concentrations.EIS measurements were performed after immersing the electrode for 30 min, the EIS spectra were collected at the open circuit potential (OCP), the peak-to-peak voltage of the AC signal was 10 mV, and the resonant frequency evaluated was 0.01-10 5 Hz.The important variables derived from the analysis of the Nyquist diagram are the resistance of charge transfer (R ct ) and the capacity of the double layer (C dl ).

Surface analysis SEM analysis
CS surface morphology and elemental composition were studied by scanning electron microscopy (SEM) Model (Quanta 250 FEG, originated in FEI Company in the Netherlands) with and without organic inhibitors.

AFM analysis
The micrographs and surface roughness of CS with and without the optimum concentration of organic inhibitors were investigated on the nanosurf C300 software of version 3.5.0.31 by employing AFM in contact FlexAFM3 mode with a nonconductive silicon probe.

Quantum chemical calculations and Monte Carlo simulation studies:
Using the Material Studio D-MOL3 program, quantum chemical calculations were used to investigate the effectiveness of the trimethoxyphenylfurylidenepyrimidinone derivatives' ability to suppress corrosion.Density Functional Theory (DFT) was utilized for the calculations, with the basis set DNP (4.4) function GGA.The COSMO solvation model was also employed.By using DFT, the quantum chemical parameters E HOMO , E LUMO , and ∆E were derived and examined.In order to identify the adsorption configurations of four investigated inhibitors on the interface of Fe (110), MC simulation was employed.Whereas, all computations were employed using the force field COMPASS (Condensed-Phase Optimized Molecular Potential for Atomistic Simulation Study).

Corrosion measurements WL method
The WL method investigates the impact of dosage on the rate of corrosion of CS in 1.0 M HCl at different temperatures and well as lack diverse inhibitor doses (Fig. 2).The examination of the data in Table 3 displays that the CR of CS declines meaningfully and the η increases significantly with increasing the concentration dosages of inhibitors from 1 × 10 −6 M to 11 × 10 −6 M, this is due to the formation of a protective coating on the CS surface [47][48][49].The inclusion of hetero nucleus atoms (N, O and S) in these tested molecules may be responsible for the efficacy of the inhibition process; as these atoms enhance the adsorption on CS via free electrons, which is crucial for the inhibition process [50].

Effect of temperature
During a three-hour immersion, the WL method was used to examine the impact of temperature on the percentage η at various temperatures ranging from  ) 1000/T, (K -1 )

(c) HM-1224 (d) HM-1221
Fig. 3 Arrhenius plots for CS corrosion in the 1.0 M HCl without as well as after using various concentrations of a-d and ∆S * embodies the enthalpy and entropy of activation, whereby h represents Planck's constant.While, the relation between Arrhenius plots of (log k corr ) vs. (1000/T) for corrosion of metal in acidic medium of different doses of the inhibitors at diverse temperatures (30 − 50 °C) was represented in Fig. 3, and the straight lines were gotten with the slope (− E a * /2.303R) as well as intercept of log A. In the same context, the higher values of E a * in the presence of inhibitors is attributed to that the physisorption mechanism [54] as shown in Table 4. Studying graphs of the transition state of (log k corr /T) vs. (1000/T) for the inhibitors are presented in Fig. 4. The straight lines with a slope = − ΔH * /R were achieved using ΔH * and ΔS * values.Whereas, a positive value for ΔH* suggests that the manufacturing of an activated complex is endothermic [55,56] as shown in Table 4, whereas a negative value for ΔS* refers to the order is determined by the transformation of reactants into an activated complex [57,58].It is evident that for the inhibited solution the ΔS * values are less negative compared to the uninhibited, as the rational probability attributed to desorption of H 2 O from the CS surface.

Study the adsorption isotherm
On the basis of mechanism of corrosion ' , it is essential to understand how the inhibitors adsorb on the CS surface.The adsorption process could be explained as a substitution process between the organic molecules in the aqueous phase (Org (sol) ) and H 2 O molecules previously adsorbed on the metal surface (H 2 O (ads) ), the adsorption mechanism is accomplished according to the following equation.
It is essential to understand how the inhibitors adsorb on the CS surface.As the reaction between organic hybrids in the aqueous phase (Org aq ) and the H 2 O molecules underwent a similar manner to this adsorption according to following equation [59]: where x refers to the quantity of H 2 O molecules that the inhibitory molecules have displaced.Adsorption isotherms are helpful for investigating the interaction between the inhibitor molecules and the metal surface.Different isotherms, involving Langmuir, Frumkin, Temkin, Florry-Huggins and Freundlich were performed to determine the adsorption type that corresponded to the tested inhibitors.It is an evident that the correlation of the Langmuir isotherm is almost equal to unity (Fig. 5) shows that the Langmuir adsorption isotherm is obeyed when inhibitors are adsorbed on metal surfaces.Additional adsorption isotherms are discussed in Table 5 and showed in Fig. 6.The following Eq. was used to obtain the Langmuir adsorption isotherm [60,61]: whereas, the defined symbols in Eq. 7 are adsorption equilibrium constant (K ads ), and the corrosion inhibitor dose in the solution (C inh ).This equation was used to calculate the value of standard free energy of adsorption (∆G°a ds ) associated with K ads for understanding of the inhibitors' adsorption process and their types [59,60]: whereas, T is the thermodynamic temperature (K), R is the universal gas constant, the molar concentration of water is 55.5.In addition, K ads values are moderately high, indicating a strong inhibitors adsorption on CS [62] as illustrated in Table 6.Also, the highly negative value of ( 6) ∆G°a ds demonstrates the adsorption occurs spontaneously [63].According to the literature, if ΔG°a ds values at around (− 20 kJ mol −1 ) or lower negative, the adsorption of an inhibitor is a physisorption.In contrast, if the values of ΔG°a ds are (− 40 kJ mol −1 ) or higher negative is defined as chemisorption [64,65].From Table 6, the ∆G°a ds values of the synthesized scaffolds are round − 26 to − 20 kJ mol −1 , indicating clearly that the mechanism is physisorption forming strong bonds.The Van't Hoff equation is used to calculate the heat of adsorption (ΔH°a ds ) (Eq. 9) [66]: Figure 7 revealed the plots of Log (K ads ) vs. 1000/T for inhibitors.Whereas, straight lines were attained with a slope = − ∆H°a ds /2.303R in which enthalpy were computed from and intercept = − ∆S°a ds /2.303R − log (55.5).Gibbs-Helmholtz equation is used to determine the standard adsorption entropy (ΔS°a ds ) at diverse temperatures [66]: log(K corr /T),mg cm -2 min -1 K -1 1000/T, (K -1 ) Fig. 4 Kinetic transition state plots for CS dissolution in 1.0 M HCl without as well as after utilizing various doses of inhibitors a-d Table 6 lists the values of K ads , △G°a ds , enthalpy of adsorption (∆H°a ds) , and the standard entropy (ΔS°a ds ).Whereas, the ΔH°a ds values are negative proving that the adsorption process is exothermic reaction [67], and the negative values of ΔS°a ds result from substitution process can be assigned to rising of entropy at the metal/solution interface due to replacing of the water molecules by inhibitor molecules in the solution [68].As the deterioration of the CS with corrosive layers on its surface was developed due to the fact of dissolution of the oxide film on the metal surface.From the OCP curves, it is noted that the potentials of inhibited solutions moved to more positive values contrasted to the uninhibited.

PDP technique
Polarization measurements were performed for investigation the kinetics of cathodic and anodic reactions.As indicated in Fig. 9, it is clear that the presence of inhibitors causes a marked decrease in the corrosion rate.The inhibitors have a significant effect on the rate of the hydrogen evolution and anodic dissolution reactions i.e. the investigated inhibitors act as mixed type inhibitors.the extrapolation of the polarization curves yields the electrochemical corrosion parameters like (i corr , E corr , β a , β c and η) which are reported in Table 7. Also, i corr values are utilized to calculate η (Eq.11) [69]: Where as, i corr and i corr (inh.)refer to the corrosion current densities in acidic solution in the absence in addition to existence of organic molecules, respectively, while (β a ), (β c ) and E corr represent anodic, cathodic Tafel and the corrosion potential.Table 7 demonstrates that the corrosion current density dropped when the inhibitors were added and η PDP increases with increasing inhibitor con- centrations.This was because the inhibitors are adsorbed (11) η PDP = i corr − i corr (inh) i corr × 100 onto the CS surface, reducing the rate of dissolution reaction by blocking active sites on the surface [70].From the measurements, it was found that the corrosion potential gap is lower than 85 mV for all concentrations, and the anodic and cathodic partial currents are also decreased.The change in the E corr value is (23 mV), these findings reveal the mixed character of the inhibitors under research [71,72] and they also suggest that the inhibitors utilized diminish the anodic dissolving rates of CS and the reduction of H + .Both cathodic (β c ) and anodic (β a ) Tafel slopes do not change remarkably, which indicates that the mechanism of corrosion reaction does not change and the corrosion reaction is inhibited by blockage of active sites by the investigated inhibitors by simple adsorption mode [73].% η PDP of these derivatives follows the sequence: HM-1223 > HM-1222 > HM-1224 > HM-1221.The results acquired from the PDP measurements are closely matched with the outcomes of WL approach.

EIS technique
EIS is used to investigate the kinetics and the surface characteristics of the electrode processes.To better mimic the non-ideal capacitive behavior of the double layer, double layer capacitance (C dl ) is replaced with a constant phase element (CPE) in the circuit, which is made up of solution resistance (R s ) in series with the parallel combination of charge transfer resistance (R ct ) Fig. 10.According to a previous study [74], the impedance of CPE is as follows: where i denotes the complex number, ω the angular frequency, ξ the proportionality factor and n the exponent of the CPE.Nyquist and Bode graphs for the corrosive dissolution of CS in HCl solution with and without varying doses of inhibitors as depicted in Figs.11, 12, respectively.The Nyquist graphs demonstrated that with an increase in inhibitor dose, the semicircular capacitance diameter is expanded due to the charge transfer phenomena in the solution [75].EIS variables including charge transfer resistance (R ct ), capacitance of the double layer (C dl ) and η (Table 8) showing that the C dl values decrease with increasing inhibitor dose, this is due to the adsorption of inhibitors on CS surface leading to formation of a film from the acidic solution [76].It is clear that R ct values rise as the concentration of the inhibiters increase, this due to the increase in the thickness of the double layer as a result of an expansion of the double layer's thickness [77] led to a decrease in dielectric constant [78] and this indicates that η EIS % increase.The value of C dl can be determined from Eq. 13 [79]: (12) Equation 14 is utilized to calculate the inhibition efficiency based on the polarization resistance [80,81]: where R ct and R ct(inh) refer to the charge transfer resistance without and with the addition of inhibitors, respectively.The results from EIS are compatible with those acquired from the PDP analysis.The standard evaluation criteria for determining which of these compounds agreed the best with the data used: low chi-square errors (χ 2 about 10 -4 ) and low 5% for allowable elemental errors in fitting mode.Therefore, in this case, the circuit in use is acceptable.The η EIS % of these compounds follows the following order : HM-1223 > HM-1222 > HM-1224 > HM-1221.(13)

Surface analysis study Scanning electron microscope (SEM) analysis
The morphology of the CS surface was evaluated using SEM to determine whether the inhibition was caused by the growth of an organic coating.The SEM images for CS surface immersed HCl and with inhibited solutions are illustrated in Fig. 13a-f.The CS sample's surface was smoother before immersion (Fig. 13a), but due to the acidic solution's powerful attack (Fig. 13b), the surface became very coarse with significant corrosion and cracks distributed throughout after immersion in HCl (Fig. 13b).But in the presence of organic inhibitors, which have a softer and smoother surface (Fig. 13c, f ), the damage has been reduced.The development of a protective organic suppressive coating on the metal's surface is indicated by this smoother surface morphology [82,83].

EDX studies
Figure 14 depicts the EDX spectra that demonstrate the specific peaks of certain elements constituting the CS afterward 24 h in the unprotected and protected 1.0 M HCl.EDX spectra in the existence of the maximum dose of the chemicals display extra lines of carbon, nitrogen, sulfur and oxygen owing to the layer of the adsorbed chemicals on CS.From Table 9, it was found that [84]: 1-Intensities of C, O, S and N signal are enhanced and this due to N, C, S and O atoms present in the chemical composition of the inhibitors, indicating adsorption of the chemicals molecules on the surface of CS. 2-Fe peaks are suppressed in the existence of the inhibitors which is because of overlying inhibitor film [85].

AFM analysis
AFM is an effective method for examining topography of the surface which confirms the adsorption of inhibitors on the surface of the corroding metal.Figure 15a-f displays three-dimensional AFM images of the CS surface before and after the immersion of inhibitors.The roughness of the CS surface related to uninhibited solution in HCl only is 879.3 mm as average (Fig. 15b), and the surface with polishing roughness is 22.3 mm (Fig. 15a).Nevertheless, in the existence of inhibited scaffolds (Fig. 15c-f ) at the highest chosen dose (11 × 10 −6 M), the  ).These evidences show that the CS surface is smoother in the presence of inhibitors compared the absence of inhibitors due to the establishing a defensive coating adsorbed from the molecules of inhibitors that protects CS surface [86].

FTIR technique
FT-IR is a crucial analytical tool to understanding efficacious groups and characterizing bonding with metal.Certain peaks of the IR spectra are corresponding to the function groups of the substances under investigation.The characteristic peaks of active function groups for free organic compounds before (pure inhibitors) and the other peaks in the presence of these compounds after immersing CS for 24 h in 1.0 M HCl + 11 × 10 −6 M at 298 K were attained and compared to each other (Fig. 16).The data of FT-IR showed that: the peaks of the function groups of the adsorbed chemicals show a tightly shifting, this confirmed the complex formation between Fe metal and inhibitors [68] and consequently, these substances have the potential to operate as corrosion inhibitors [87,88].

Quantum chemical calculations
To anticipate the configuration and electron dispersion of trimethoxyphenylfurylidene-pyrimidinone derivatives, quantum chemical computations are employed.The evaluation of molecular reactivity is commonly performed using density functional theory (DFT).Figure 17 shows the optimized structures of the inhibitors studied.Whereby, E HOMO and E LUMO (FMOs) are crucial descriptors in chemistry for studying the chemical reactivity in various reactions, the donor-acceptor interaction between adsorbed molecules and FMOs of adsorbent atoms can give valuable insights in exploring most chemical interactions, particularly those involving compound adsorption such as corrosion inhibition properties.An increase in E HOMO values often indicates a molecule's greater ability to donate electrons to an acceptor molecule with vacant molecular orbitals.Conversely, a lower E LUMO value often associates with a higher capacity accept electrons by the reacting species.As a result, a lower E LUMO is anticipated that a molecule has a greater tendency to gain electrons in specific interactions.In this sense, E HOMO can measure ionization potential and a species' tendency to undergo electrophilic attack, while E LUMO is indicative of its susceptibility to nucleophilic attack.Therefore, an increase in E HOMO and decrease in E LUMO are expected to be typical of high corrosion inhibition properties of compounds by promoting their adsorption on metallic surfaces through chemisorbed film formation.The difference between E LUMO and E HOMO (ΔE) is a crucial stability index that is associated with corrosion inhibition capabilities in corrosive and tribological systems [89,90].
A small energy gap between HOMO and LUMO orbitals suggests a soft nature, while a large gap indicates a hard nature.Whereby, η values is enhanced this is commitment to increase the value of E HOMO and reduction in both E LUMO and ΔE.Table 10 lists the results of quantum calculations, such as both E HOMO , E LUMO and energy gap (ΔE), while other quantum chemical parameters [90,91].Based on the values on Table 10, the trend in the quantum chemical parameters shows that the increasing order of inhibition follows: HM-1223 > HM-1222 > HM-1224 > HM-1221.
The effect of corrosion inhibition effects of the four inhibitors were found to be consistent with the decreasing order of energy gap and E. In contrast to HM-1222 molecule, which has two N-H hydrophilic groups, HM-1223 compound, which has a furan ring and two ethyl groups, has stronger electron donating capacity and lipophilic qualities.Additionally, introducing (S) atom enhances capacity of molecules to give electrons by sharing their lone pair.While HM-1224 and HM-1221 has lower electron donating ability than HM-1223 and HM-1222 due to the weaker impact of their (O) atom in to donate electrons compared to S atom.

Monte carlo simulation studies
MC simulation was used to visualize the interaction between the four inhibitor molecules with the CS surface and the adsorption mechanism.Figure 18 shows the most possible adsorption configurations of pyrimidinone molecules on the CS.This could be achieved via the adsorption locator module, which exhibits smooth disposition and provides an improvement in adsorption with the greatest surface coverage.The data that were ascertained via MC simulations are listed in Table 11.The unrelaxed and relaxed adsorption energies of four  supporting the replacement of water molecules with pyrimidinone inhibitors.Furthermore, it can be summarized that these MC results correspond well with the quantum chemical calculations as well as the experimental data [10,51].

Mechanism of inhibition
The adsorption process is influenced by the inhibitors' chemical composition, surface charge, and internal charge distribution.Generally, chemisorption and physisorption-two different ways whereby inhibitor compounds can adsorb on the surface of CS are considered.Organic molecules can be adsorbed through physisorption.The electronegative donor atoms N, O, S, and π-electrons of the aromatic ring in the compounds under investigation effectively facilitate the adsorption of inhibitors onto the surface of CS.Consequently, by hydration chloride ions adsorbed on the metal surface which led to allocate the negative charges, on the other hands, acidic medium acts as positively hydrogen donating atoms.Besides, electrostatic interaction (physisorption) was occurred between positively protonated organic  molecules and negatively chloride anions adsorbed on the surface of CS [92].This surface adsorption results in a protective coating that repels water from the metal's surface and shields it from corrosion.The development of organic derivatives' adsorption was confirmed by AFM and SEM results.The inhibitors tested in previous experiments can be ranked in terms of inhibition efficiency as HM-1223 > HM-1222 > HM-1224 > HM-1221.Due to the two ethyl groups in HM-1223, which enhance the molecular size of the compound and act as atom donors, it is thought that HM-1223 is more complex than HM-1222.Due to its higher molecular size, HM-1224 is superior to HM-1221 (Fig. 19).

Fig. 2
Fig. 2 WL-time curve for CS in 1.0 M HCl with as well as without different concentrations of inhibitors a-d at 303 K

Figure 8
Figure 8 displays the relation of the OCP vs. time curves for CS in 1.0 M HCl in the absence besides utilizing varied concentrations of investigated compounds, (a) HM-1223 (b) HM-1222 (c) HM-1224 (d) HM-1221, at 298 K.As the deterioration of the CS with corrosive layers on its surface was developed due to the fact of dissolution of the oxide film on the metal surface.From the OCP curves, it is noted that the potentials of inhibited solutions moved to more positive values contrasted to the uninhibited.

Fig. 5
Fig.5 The plots of Langmuir isotherm for CS in 1.0 M HCl with altered doses of inhibitors a-d at diverse temperatures

Fig. 6
Fig.6 Various adsorption isotherms of the tested inhibitors for the corrosion of CS in 1.0 M HCl at 303 K

Fig. 7
Fig. 7 Vant's Hoff plots (Log K ads vs. 1000/T) for the adsorption of organic molecules a-d at 303 K on CS surface in 1.0 M HCl

Fig. 8
Fig.8 Changes in E OCP vs. time for CS in the 1.0 M HCl either alone or with various dosages of organic hybrids a-d at 298 K

Fig. 9
Fig. 9 PDP curves for the CS corrosion in 1.0 M HCl at 298 K without and after adding diverse concentrations of inhibitors a-d

Fig. 11
Fig. 11 Nyquist plot for CS in 1.0 M HCl and with several doses of the inhibitors a-d at 298 K

Fig. 12
Fig.12 Bode plot for corrosion of CS in 1.0 M HCl and in the existence of various doses of organic constitutions a-d at 298 K

Fig. 13 Fig. 14
Fig. 13 SEM images for CS smooth surface (a), then after 24 h immersion in 1.0 M HCl (b) and in the existence of 11 × 10 −6 M of inhibitors (c-f)

Fig. 15 aFig. 16 FTFig. 17
Fig. 15 a Represent smoother image CS surface taken by AFM, whereas, image b indicates what happened after immersion in HCl only, while, images from (c to f) refer to the presence of 11 × 10 −6 M of inhibitors Fig. 17HOMO and LUMO electron density maps for the studied inhibitors

Table 3
WL corrosion parameters of CS in 1.0 M HCl at various temperatures 303-323 K and with as well as lack various doses of inhibitors [51][52][53][54]ocking active sites by adsorption on the CS surface.Activation thermodynamic parameters were evaluated using the Arrhenius and transition state Eqs.[51][52][53][54]:where k corr represents the corrosion rate resulted from WL measurements, R denotes the gas constant, T represents the absolute temperature, E a * signifies the apparent activation energy and A indicates the Arrhenius frequency factor, N refers to Avogadro's number, ∆H *

Table 4
Activation parameters gained from WL approach

Table 5
Different adsorption isotherms of the tested inhibitors for the corrosion of CS in 1.0 M HCl at 303K

Table 6
The results of adsorption thermodynamic of organic scaffolds on CS in 1.0 M HCl at 303-323 K

Table 7
PDP corrosion parameters of CS utilizing 1.0 M HCl without and with besides utilizing diverse doses of the organic constitutions a-d at 298 K

Table 8
Parameters gained from EIS in 1.0 M HCl and with the addition of doses of the investigated additives

Table 9
Surface characteristics (wt.%) of CS both earlier and later dispersion in 1.0 M HCl with and without of 11

Table 10
List of quantum chemical parameters on the investigated inhibitor compounds